A quadrupolar nucleus is one that has a quantum spin number greater than ½. Such nuclei have a lower symmetry than
spin-½ nuclei. The quadrupole moment that varies between nuclei is a measure of this asymmetry.

Their energies split upon the application of a magnetic field into multiple levels (fig. 1). By comparison, spin-½ nuclei
split into only two levels. The number of levels is given by 2n + 1 where is the spin number. The
different splitting patterns can be seen in their coupling with other nuclei.

Fig. 1. Energy level diagrams for nuclei of different spins

The NMR signals of quadrupolar nuclear are usually wider than those of spin-½ nuclei due to rapid quadrupolar
relaxation. The line-width increases with the
line-width factor that is related to the quadrupole moment of
the nucleus, the size and asymmetry of the molecule. For example,
deuterium has a small
line-width factor of 0.41 fm4 with a quadrupole
moment of 0.286 fm2 and yields a line-width in HOD of 1.7 Hz while
17O has a line-width factor of 2.1 fm4 with a
quadrupole moment of -2.56 and yields a line-width in H217O of 69 Hz. Some nuclei such as
197Au and 201Hg yield signals too broad to be observed with a high-resolution NMR
spectrometer. The effect of shape and size of the molecule can be demonstrated with 14N-NMR (fig. 2).
NH4+ is small and highly symmetric yielding a line-width of 0.8 Hz, NH3 is also
small but asymmetric giving a line-width of 16 Hz. Urea is larger and even less symmetric yielding a line-width of
982 Hz.

Fig. 2. Comparison of line-widths of 14N signals. The larger
and less symmetric the molecule, the wider the signal.

In solid-state NMR, the
methods applied to quadrupolar nuclei differ from those
applied to spin-½ nuclei. There is also a difference between whole integer and half integer nuclei. Whole integer nuclei yield very broad spectra while half integer nuclei yield a relatively narrow central transition in addition to a very broad multiple quantum signal. The central transition can be used to yield high-resolution information from the spectrum.